JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE SEPARABLE WEAK BOUNDED APPROXIMATION PROPERTY
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
THE SEPARABLE WEAK BOUNDED APPROXIMATION PROPERTY
Lee, Keun Young;
  PDF(new window)
 Abstract
In this paper we introduce and study the separable weak bounded approximation properties which is strictly stronger than the approximation property and but weaker than the bounded approximation property. It provides new sufficient conditions for the metric approximation property for a dual Banach space.
 Keywords
the separable weak metric approximation property;separable weak metric approximation property with conjugate operators;weak Radon-Nikodm property;metric approximation property;factorization lemma;
 Language
English
 Cited by
1.
Nuclear Pseudo-Differential Operators in Besov Spaces on Compact Lie Groups, Journal of Fourier Analysis and Applications, 2017, 23, 5, 1238  crossref(new windwow)
 References
1.
P. G. Cassaza, Approximate properties, In: W. B. Johnson, J. Lindenstrauss(eds.), Handbook of the Geometry of Banach Spaces, Volume 1, 271-316, Elsevier, 2001.

2.
C. Choi and J. M. Kim, Weak and quasi approximation properties in Banach spaces, J. Math. Anal. Appl. 316 (2006), no. 2, 722-735. crossref(new window)

3.
C. Choi and J. M. Kim, Hahn-Banach theorem for the compact convergence topology and applications to approximation properties, Houston J. Math. 37 (2011), no. 4, 1157-1164.

4.
T. Figiel and W. B. Johnson, The approximation property does not imply the bounded approximation property, Proc. Amer. Math. Soc. 41 (1973), 197-200. crossref(new window)

5.
A. Grothendieck, Produits tensoriels topologiques et espaces nucleires, Mem. Amer. Math. Soc. 16 (1955), no. 16, 140 pp.

6.
J. Johnson, Remarks on Banach spaces of compact operators, J. Funct. Anal. 32 (1979), no. 3, 304-311. crossref(new window)

7.
K. Y. Lee, Dual spaces of compact operators space and the weak Radon-Nikodym property, Studia Math. 210 (2012), no. 3, 247-260. crossref(new window)

8.
A. Lima, O. Nygraard, and E. Oja, Isometric factorization of weakly compact operators and the approximation property, Israel J. Math. 119 (2000), 325-348. crossref(new window)

9.
A. Lima and E. Oja, The weak metric approximation property, Math. Ann. 333 (2005), no. 3, 471-484. crossref(new window)

10.
J. Lindenstrauss and C. Stegall, Examples of separable spaces which do not contain ${\ell}_1$ and whose duals are non-separable, Studia Math. 54 (1975), no. 1, 81-105. crossref(new window)

11.
K. Musial, The weak Radon-Nikodym property in Banach spaces, Studia Math. 64 (1978), no. 2, 151-174.

12.
E. Oja, The impact of the Radon-Nikodym property on the weak bounded approximation property, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. 100 (2006), 325-331.

13.
R. A. Ryan, Introduction to Tensor Product of Banach Spaces, Springer, London, 2002.